Crystalline color superconductors

Abstract

Inhomogeneous superconductors and inhomogeneous superfluids appear in a variety of contexts including quark matter at extreme densities, fermionic systems of cold atoms, type-II cuprates, and organic superconductors. In the present review the focus is on properties of quark matter at high baryonic density, which may exist in the interior of compact stars. The conditions realized in these stellar objects tend to disfavor standard symmetric BCS pairing and may favor an inhomogeneous color superconducting phase. The properties of inhomogeneous color superconductors are discussed in detail and in particular of crystalline color superconductors. The possible astrophysical signatures associated with the presence of crystalline color superconducting phases within the core of compact stars are also reviewed.Comment: Added 3 figures, added section II F, added section with conclusions. Several references added. Improved the quality of the presentation and removed various typos. Almost matches the version accepted for publication of Reviews of Modern Physic

Inhomogeneous chiral condensates

“…(27) in the deconfined phase where =¯ = 1, while in the confined phase, =¯ = 0, the thermal excitation of quarks is strongly suppressed. The total thermodynamic potential of the PNJL model is then given by…”

“…(27) can be used to calculate the thermodynamic potential. The result is, of course, identical to one presented in Chapter 4.…”

“…As discussed in the Introduction, nonzero isospin chemical potentials are known to have large effects in color superconductivity, where they hamper the BCS pairing of up with down quarks [147], possibly leading to inhomogeneous pairing patterns [25,27]. Moreover, it has been suggested that an unequal chemical potential for up and down quarks could lead to two separate chiral phase transitions [148,149,150], although this effect was found to be suppressed by the chiral anomaly [151].…”

“…Since the 2SC phase involves the pairing of up with down quarks, it is rather sensitive to isospin asymmetries, and could therefore be suppressed in compact stars [147,177,178,179]. In this case, inhomogeneous color superconducting phases might become favored [27] and it would be interesting to study this possibility simultaneously with inhomogeneous chiral condensates.…”

“…Charge and spin density waves are commonly found in solid-state physics (for a review see, e.g., [22]), and crystalline phases have also been discussed long time ago for superconductors by Fulde and Ferrell as well as by Larkin and Ovchinikov [23,24] and more recently for color superconductors [25] (see also [26,27] for reviews). Inhomogeneous phases have also been shown to appear in imbalanced cold atom Fermi gases [28,29].…”